While this is always true, it is possible to get a longer object in if you turn as you go. It's an easy problem if the object has no thickness, but trickier otherwise.
Note that we're still being possibly inefficient, as we are not using our third available dimension; however, this is only relevant if the box is much longer in one direction than the other two (for example, if you were trying to carry a 2x4 around this corner).